Fall 2001 16.3116-1 Estimators/observers . Problem: So far we have assumed that we have full access to the state a(t)when we designed our controllers Most often all of this information is not available Usually can only feedback information that is developed from the sensors measurements Could try“ output feedback” K KI ame as the proportional feedback we looked atat the beginning of the root locus work This type of control is very difficult to design in general Alternative approach: Develop a replica of the dynamic sys- tem that provides an estimate of the system states based on the measured output of the system ● New plan 1. Develop estimate of a(t) that will be called a(t) 2. Then switch from u=-Ka()to u=-kit ●1 wo key questions How do we find i(t)? Will this new plan work?Fall 2001 16.31 16—1 Estimators/Observers • Problem: So far we have assumed that we have full access to the state x(t) when we designed our controllers. — Most often all of this information is not available. • Usually can only feedback information that is developed from the sensors measurements. — Could try “output feedback” u = Kx ⇒ u = Ky ˆ — Same as the proportional feedback we looked at at the beginning of the root locus work. — This type of control is very difficult to design in general. • Alternative approach: Develop a replica of the dynamic sys￾tem that provides an “estimate” of the system states based on the measured output of the system. • New plan: 1. Develop estimate of x(t) that will be called ˆx(t). 2. Then switch from u = −Kx(t) to u = −Kxˆ(t). • Two key questions: — How do we find ˆx(t)? — Will this new plan work?